But this is exactly what America's legendary Tuskegee Airmen did, more than 60 years ago. While they were fighting the Nazis abroad, they were battling racism at home.
Their double victory has been honoured by Congress, which has presented the survivors of America's first black air squadron with the Congressional Gold Medal.
The medal, which is the highest civilian award bestowed by Congress, can also be awarded to military personnel.
The venue itself, the Capitol Rotunda, was symbolic: once, these men would have been banned from entering because of the colour of their skin.
Desegregation
Now, they have been honoured not only for their outstanding war-time record, but for the groundwork that they helped lay for the civil rights movement.
We proved something different, not only in aviation history but also in American social history 
"For all the unreturned salutes ... I salute you for the service to the United States of America," President George W Bush said, as he presented the medal.
Retired Air Force Colonel Charles McGee - now 87 and one of about 350 Tuskegee veterans to make the trip to the Rotunda - told the BBC News website why the medal ceremony meant so much to him.
"It's a great feeling because it's been a great number of years - a little better than 60 years - since our activity," he said.
"It was one that wasn't expected to be successful - but we proved something different, not only in aviation history but also in American social history."
It was partly thanks to the airmen's courage, determination and skill that President Harry Truman signed an order desegregating the army in 1948. This was some 15 years before civil rights leader Martin Luther King marched on Washington.
During World War II, the Army had become the country's largest minority employer. However, units, training and facilities were segregated.
The prevailing view at the War Department was summed up in a 1925 study by the Army War College: that African-Americans "were cowards and poor technicians and fighters, lacking initiative and resourcefulness".
In 1941, however, Congress forced the Army Air Corps to create an all-black combat unit.
The army reluctantly agreed and sent the unit to a remote air field in Tuskegee, Alabama, keeping them separate from the rest of the army. This became the training ground for some pilots - numbering almost 1,000 - navigators, mechanics, and ground crew.
Over the years, some 14,000 people came to serve in what is now called the "Tuskegee Experience".
It took months, however, for the army to let any of them see combat.
Col McGee, born in Ohio and raised in Illinois and Iowa, said the airmen were aware that they were breaking new ground in the struggle for equal rights, although they did not set out to spark a social revolution.
"Clearly we didn't get together to say 'Let's go down to Alabama and set the world on fire'," he said.
"Individuals all across the country were really just very interested in being accepted for who you were, being given an opportunity before being told you couldn't do something just because of your of birth."
'Black Birdmen'
The first group was known as the 99th Fighter Squadron. They flew ground attack missions in North Africa and participated in the destruction and surrender of Pantelleria, off Sicily. They were later joined by other units to make up the 332nd Fighter Group.
According to military writers, the group were both feared and respected by the Germans, who called them the "Schwarze Vogelmenschen" (Black Birdmen).
And their battles did not end with the Nazis. At home, they challenged institutionalised racism.
One of most citied incidents was in 1942, when a large group of Tuskegee Airmen tried to enter a whites-only officers' club at the Freeman Air Field in Indiana, against direct orders for them to stay out.
One hundred and three officers were arrested, charged with insubordination and ordered to face court martial. The charges, however, were quickly dropped. Some 50 years later, survivors were told that their military records had been purged of any reference to the incident.
According to the website Tuskegee Airmen Inc, after the WWII ended in 1945, the black airmen returned to the United States to face continued racism and bigotry despite their outstanding war record.
It was not until 1949 that the Air Force ended segregation and the Tuskegee Airmen were scattered among other units. Even then their struggle was not over, said Col McGee, who also served in Korea and Vietnam.
It wasn't fun coming home and coming down the gangplank and seeing 'whites this way, blacks that way
"Change often comes about slowly, so there were still those who weren't happy. But as we were able to show technical and leadership abilities, acceptance finally came about and became widespread.
"Had we not been successful, certainly then we would have had the folks saying 'we told you so' - it wouldn't have been an early step in the civil rights movement.
"But [our success] made it possible for President Truman to issue orders mandating all of the service to integrate.
"It wasn't fun coming home [from WWII] and coming down the gangplank and seeing 'whites this way, blacks that way'.
"But we persevered and it's great that the government realised it and we're receiving this honour today."
It was not until the 1970s that the airmen's story began to be told more widely. A film about their exploits was released in 1995 and director George Lucas has been working on a movie about the men called "Red Tails" - after the tails of their aircraft that were painted red.
There is little doubt that their prowess in the skies helped dispel many of the negative stereotypes that were the order of the day.
These were young, mostly college-educated men, who were charismatic in front of the cameras.
And their courage is seen as having helped to change the attitudes of a nation.
