Politics is kind of over my head. In the case of the civil war, I've never really become attached to either side. I figure I'll do it this playthrough though. My character also has no side to be attached to. So I was thinking, maybe her husband can influence her choice.

So, are there any husband that are clearly one side or another?

If you're looking for a role-play element then whoever you escaped Helgen with could influence your choice? say you escape with Hadvar and join the imperials you do various quests with him and form a strong friendship

This is a tricky topic, as I've not yet found a husband who voices his opinion on either side of the issue. However, If you're a role player type, you can just assume that your husband supports your decision. Something that I've done before, is marry someone, and then have them follow me. After that, you can dress them in Imperial/Stormcloak armor to show others whom you both support. They will accompany you on vital missions for whichever side you choose, thus making it more realistic, as they are fighting for the same cause as you. As for choosing which side to ally with, look at their ideals and convictions and compare them to yours.

Take a look for yourself: http://www.uesp.net/wiki/Skyrim:Marriage#Male_NPCs

Should be what you are looking for.

Any non-nord would be agaisnt the Stormcloaks, I'd imagine.
But not any Nord would be supportive of the Stormcloaks, either.