Just got back a few weeks ago with a family of 4....
For my daughter and son it cost $200 each to complete their Open Water referral with Coconut Tree Divers. - 4 dives in 2 days. My son went on to complete his Advanced Open Water in 2 more days for $280 - 5 more dives in 2 days (night dive was on Thursday). He had completed all the reading for the AOW prior to our arrival in Roatan. All the dive shop prices are pretty competitive. All your rental gear is included in the course dives. Additional dives would be $25 - $30 depending on the number of dives. If you are really looking to save money, you can get complete OW course in Roatan for a cheaper then doing part at home and the referral portion in Roatan. Not my first choice on a Honey Moon, but it is all about priorities.
We stayed at Sundancer's in West Bay and rented a 3 bedroom Cabana, 2 bathrooms, kitchen, etc. for $850 it was very much like renting a nice cabin in Wisconsin or Minnesota. You could probably get a much smaller one for $600. Recommend you talk to Lynn and Bob Milsaps. You would need to allow for cab fare back and fourth unless you rent a car, but cab fare is pretty cheap. We rented a car mostly from a logistics standpoint because we like to explore and dealing with logistics of 4 people on different schedules.
That leaves about $400 - $500 for food if you only do 4 dives each. You can definitely eat for reasonable prices, we took advantage of the kitchen for breakfast, bought eggs, fresh fruit from street vendors, etc. Lunch - so many choices in West End, but Sun Downers is a must for lunch, on the beach, great food - grilled chicken sandwich for $8 and relatively quick service at that time of day. Dinner - depends on what you want - prices are comparable to prices in the states, seemed a little cheaper on the higher end food.
If you decide you like diving after your OW course (keep in mind you will be doing drills in the first 4 dives that make the dives not quite as much fun), I would move directly to the AOW course and spend the money from the additional fun dives on the course. The AOW dives still have drills, but have more "fun" time as well. You can complete your OW in 2 days, take a break and then do your AOW in 2 - 3 days and still have time to blow on more dives.
You can also see a lot of great stuff snorkeling in front of Sun Dancers, a couple of our snorkel trips were better then some of the dives I did from a sea life stand point.
If you want to save some money on diving and lodging check out Atlantic Sea Divers. My son and I took a walk one day and stumbled into to them. I was very impressed by their service oriented dive operation. They offer a package for diving and lodging that was in the $550 range for a week. We checked out a room with 3 beds for the future, would not work for our family because that is what it was - a room with 3 beds and bathroom, but you might be able to find a room for 2 that works. The package deal had a learn to dive option as well. There website not much to look at, but their location is good and the grounds around their cabins are very nice and right on the beach. Ask for Carlos he is their manager.
Good luck if we could find cheap airfare to Roatan we would definitely go back sooner then later.