I like the idea of asking on a marriage-related forum.
Three months seems way too long to me, but everyone is different. I have a couple of happily married friends who have spent months at a time living in separate countries. I know someone, not even a cyclist most of the time, who thought he'd like to use the time between graduating and starting work to bike the Southern Tier. If I remember correctly, his wife flew out around halfway, and they spent a few days together.
For my part, my wife and I have taken separate vacations a couple of times, because of availability of time off and other factors, but I think they max out at a couple of weeks. Also for the last two years, we have taken a week off together at the beach, but I leave a few days early on my bike, and we meet up at the coast. So short trips, a camping weekend, or a trip to visit family are not a big deal, but I'd have reservations about doing a longer trip. But everyone is different.