I guess ultimately it depends on the kind of relationship the OP has with his friend and his friend's wife.
What I dislike about the idea of asking my husband first instead of at the same time is twofold. First, the idea that my husband knows first that someone likes me, when I feel I should be the first person to know (tied first, in this case). Secondly, and the more important one, it's the idea that my husband could say "no, not a good idea" and that I wouldn't be told what happened behind my back, and have no control over it. Someone else would have made a decision about my life without consulting me first.
I think everyone should always have the option to make an informed decision. If someone wants to date me and my husband says no, I want to be aware. I might decide to divorce my husband over it, for all we know. I think hiding that kind of thing from me is a form of cheating, and I would feel very betrayed.
If my husband went to me first thing and asked what I wanted to do about it, then I wouldn't be upset with my husband, but I would still be upset with his (our) friend.
I do feel the proposal example is close: if the father says no it means no, if he says yes you can go on and propose to your girlfriend (who always has the option to say no as well). But the idea that the father or husband is a first step rather than a step to be taken at the same time (in the case of a husband) or not a step to take at all (in the case of a father) is I feel disrespectful of the spouse.
We're not talking about people who like each other and are asking the husband if it's okay. We're talking about someone who hasn't disclosed his feelings yet. What is he going to do if the husband isn't comfortable with it? Tell the wife "I like you but your husband doesn't want me to date you", which is putting them against one another? Or lie, which is disrespectful considering her husband already knows, and she'd be denied the right to know about something that concerns her when a third party was told already? Talking to the husband first is putting himself in a bad position with no good answer if the husband was to say no.
It's also putting the husband in a position where he might be blamed for making two people unhappy by making the decision himself on his own. If the decision comes from both of them at once (regardless of who said "no" to it), then it seems to me it would be less harmful to both the relationship and the friendship.
For the same reason (the last one), I believe talking to her first would be a bad idea, as if she is fine with it, it would also put the husband in a position of saying no to both of you and taking all the blame for it not being an option.
I personally believe telling the wife first, although a bad idea, would be the least worse of the two. If it happens, both have to say yes, and the order isn't that important. But if it doesn't happen, the wife saying "no" and therefore the husband not being asked isn't as big a deal as the other way around: it's her life, not his. Ultimately, even if he isn't fine with it, it's still her choice, not his. I'm not suggesting she would do something that makes her husband uncomfortable, or that the OP would be fine with it in any way, but in theory, ultimately it's her life, her choice, and other people's opinions and feelings are just influences on her decision, nothing more.
It seems to me we have strong disagreement on the issue, which I assume is because I see myself in the position of the wife and you see yourself in the position of the husband. While I can imagine my friends telling me first that they like my husband, I can't imagine giving any answer other than "why the hell are you asking ME for?"