This already happens, quietly. This is why there are, in fact, Canadians in Iraq right now. About 50 I believe. Every spring, my friends in the PPLI (Princes Patricia Light Infantry) are sent down to Virginia for training. And a lot of other units train there as well.
This was also actually a recommendation I made in a policy paper for a Poli Sci class a while ago (I was one of about 10-15 conservatives out of 200+ students. I got one of the only As on the policy papers though.) Integration is the only way I think we can survive as a military at this point, without spending more money. Ill try to dig up the paper tonight.
Integration might save the US money, too. Let's say, for the sake of argument, the Canadian military specializes in search and rescue or military policing (a sorely needed speciality, from what I've heard). That's one specialist area that the US military doesn't have to spend its money one.
The US military is having money problems, too. It would be great for everyone involved if allies could take over certain areas.