Can you combine the cervical cap/diaphragm with hormonal birth control?!

I've never seen any reason why you couldn't but I've never heard of people doing it. I was considering this in my last relationship because my boyfriend just could not keep an erection when he tried to put on a condom. Just as soon as he tried to put it on, or got in on he went flaccid. I was on birth control and I still am, but I was always really nervous not using a condom because of the added pregnancy protection. So I wondering if anyone has done this or tried to? I'm not really concerned about it anymore because my current boyfriend doesn't have any of those problems, and we use condoms whenever we're not sure of birth control (like if I'm on antibiotics or something). But I would like to know for future reference if you can combine those two options if condoms aren't working for you, so you get that added barrier protection. I really wouldn't want to try female condoms if anyone recommends those, I've seen them and considered them and I just can't get over how gross they are to me..