Well well, this is an intriguing topic.
Okay, taking a look at this 'third hand smoke' silliness. Indoor air is almost always less clean than outdoor air. Particulate matter, VOCs, mold count, etc. I assume your husband has already had an air quality survey done of your place of residence, and taken steps such as proper ducting and venting, cleaning of ducts and vents as needed, and has a high quality filter in your HVAC system. This should really be his main focus if he's truly worried about air quality.
Also, we're looking at a major difference in harmful byproducts. The only big one popping out at me in e-cigs would be residual nicotine, where as cigarette smoke has a laundry list of
bad things. It is possible that if you have poor air circulation, you could have some of the vapor and nicotine deposit on floor surfaces. I think that nicotine will degrade/oxidize in normal oxygen environments, and at least on hard surface floors you're already probably cleaning it off with mopping. I'm not sure if a vacuum will remove all of it from carpeting, but it probably helps. VapinDove, you can tell your husband if he's worried, he really should stop licking the carpeting, not only might it have a little nicotine, it probably has all other sorts of nasties.
Much of the worry about dermal or ingested content would probably be due to the fact that cigarette smoke tends to add a nice layer of tar to everything. Vapor, of course, does not. It is somewhat possible that your husband may be getting a small amount of nicotine from your vaping byproducts, but if nicotine is what he is worried about, please make sure that he never eats potatoes, carrots, beets, peas, green beans, lima beans, broccoli, cauliflower, cabbage, spinach, asparagus, celery, cucumbers, green peppers, lettuce, onions, radishes, tomatoes, cayenne, eggplants, or many other foods.
As for PG deposits, it's not anything to worry about. Though PG is less volatile than water, it will indeed still evaporate. Other substances in e-cig vapor are probably beyond worry when considering other indoor air contaminants and chemical and microbial dangers on surfaces.
If he remains unreasonable on the topic... well, frankly, I'm not sure. I still think you should make him prove the harm to him taking into account everything above before you have to leave your house to take a puff. You already made a huge jump in his direction by quitting cigarettes, he should meet you in the middle somewhere.