There were some female officers during WWII. I'm specifically thinking of Susan Ahn who was a naval aviation instructor and who made lieutenant shortly after the end of the war. But they were exceptionally rare. There were also women who served in something more like a command position, like Florence Blanchfield who served as Superintendent of the Army Nurse Corps during World War II. She was made a permanent lieutenant-colonel in 1947.

But a woman (and a foreign national at that) holding a independent command over men? Let alone acting in combat roles? No. I'm not aware of any women who were able to achieve that.

So, this is only a single primary source, but Instructions for American servicemen in Britain, 1942, ostensibly a handbook issued to US soldiers and sailors posted to the UK during the war, had this to say:

British Women at War. A British woman officer or non-commissioned officer can and often does give orders to a man private. The men obey smartly and know it is no shame. For British women have proven themselves in this war. They have stuck to their posts near burning ammunition dumps, delivered messages afoot after their motorcycles have been blasted from under them. They have pulled aviators from burning planes. They have died at the gun posts and as they fell another girl has stepped directly into the position and "carried on." There is not a single record in this war of any British woman in uniformed service quitting her post or failing in her duty under fire.

Now you understand why British soldiers respect the women in uniform. They have won the right to the utmost respect. When you see a girl in khaki or air-force blue with a bit of ribbon on her tunic-remember she didn't get it for knitting more socks than anyone else in Ipswich.

Just a side-note - Agent Carter (presumably the woman you're referring to) was a British agent, not American, and was serving in a special operations role for the SSR (fictional group similar to OSS) in presumably a joint effort with the US Army.

I don't know how the US military handles liaisons like this, especially internationally.