At one time I was an interpretive naturalist, and managed a nature center for a state park. Not only did I witness adults who were not keen to the outdoors, I had children not overjoyed as well. I was on a crusade to change that situation. Many times it was one nature loving parent, who tried to inspire a family member to step on over to the other side. Steps is a good metaphor, as I found small gradual steps, or bites can work a lot better than instant total immersion. A lot of it can be how far and fast folks can expand their comfort zone, and also many times deal with potential fears/phobias that can go hand-in-hand.
I had visitors who wanted to go boating, but were afraid of the water snakes, go hiking but afraid of ticks... I found by providing an education to these concerns, and measures to deal with them as with any concern in life, helped alleviate some of the stress. As for programs I did, that I found were particularly enjoyable to "non-outdoorsy' people were:
Fishing: Low physical impact to reward ratio, easy participation for all family members. Never once did I not see an ear-to-ear smile on the face of a person catching their first Bluegill. Never.
Star gazing: I had a volunteer bring his massive reflector telescope, and guests could see the rings of Saturn, moons of Jupiter, or even the moon at HD. This stuff is magical, and profoundly binds you with the universe.
Night time owl call ins: I would have a specialist from the raptor rehab center perform a pre-easy hike talk, them we would venture into the woods, to call in Barred Owls. We would get single and pairs almost on top of us, doing their incredible calls. You never heard them fly in, and talk about a magical moment, when these owls would start their 'monkey call'. I know this experience will live forever with many of the attendees.
Perhaps a nice visit to a local nature center, would be a spark for you husband.