I take a deep breath before I (try to) answer this. Only because I don't want you to take my word for it. Ask them. Sadly, you may get a different answer from what the person on the phone tells you to what the person at the window on the day wants from you. I'll share my opinion and my experience...but do remember that at the end of the day, you are to provide the papers they want. It's really supposed to be to the letter.
Firstly, we are (thankfully) two nations that have a great relationship right now. As a result, some of the things that come from history as being legal standard in one country, are often accepted in the other. Take notarization, for example. The US has Notary Publics that stamp documents to "legitimize" them. They don't need to know you, they just have to have seen you sign it and show some ID. The UK will "legitimize" something if it is countersigned by someone of good stature in the community and who has known you for two (three?) or more years. Since you will be applying at a British Consulate for the visa, I really don't think that it will be too much trouble for them to accept your husband getting that document to you in "the British way". In other words, if he takes a copy of his birth certificate and has someone sign with all the official stamps and signatures, there should be no reason why this would not be accepted at the consulate as "a notarized copy" (he can also request a 2nd original copy of it). Again, my opinion.
My other comment is a bit more "keep your fingers crossed" advice. When my husband and I went to the British Consulate in New York to apply for my spouse visa, we sat in the queueing/waiting area, huge box of everything we could possibly think of in lap, among other people wanting the same thing: some sort of visa. We seemed to be the most prepared. Many were there singly. From our position (and everyone else's) you can't possibly avoid hearing what's going on up at the windows. Having had that prior "peek" to the first screening process, we approached with full confidence. You see, it was astounding that some people were so completely unprepared. Some didn't even bring passports, or marriage certificates. Some couldn't prove they had any place to live. Others couldn't prove financial support. A lot of these people completely missed the point of what they needed to prove. I do not know if they got turned away. But I do know that when it was turn for my husband and I to go up there, you could tell the people at the window were very happy that we seemed to have it all in order.
My point in what I just said is that you have a copy of his birth certificate. And you have his original passport. The only hiccup is that you didn't get the copy notarized. Unless you get someone in a really bad mood, I don't think you have a problem.
For all the sweat we went through beforehand, we were amazed the process wasn't more torturous. It's almost as though you walk out wishing there had been some fingernail pulling to justify the huge worry that lead up to it. You walk out astounded "Is that it?". However, you are put through those worrying stages for good reason. It makes you check and double check your list of documents to support what you say. Do read the intructions carefully, and try to follow them to the letter. The answers are all there. That's the best advice I can give.
