We recently started looking into our options to move to Bulgaria

Since you are married he does not need a work permit, but he does need a D-visa and he MUST get the d-visa at the Bulgarian consulate closest to his residence (meaning he cannot get one over here). He also does not have to pay the visa fees and getting a visa should be easy- the most difficult part is getting his FBI check apostilled. You will also need copies of your marriage certificate and your children's birth certificates.

Once he comes to Bulgaria, he will have to get a residence permit within 3-6 months. (The sooner the better). He will need everything he needed for a D visa as well as proof of insurance, proof of address in Bulgaria (It is easiest to get a rental contract in his name, so you don't have to write out an extra letter saying you allow him to live with you), and proof that he can afford to live in Bulgaria for a year (Either a work contract or a Bulgarian bank account in his name with the minimum wage for a year in it --- I think it is something like 5000 bgn now, but not quite sure). For me, each year to renew my permit cost around 1000 lev (550 for the fee, 30-90 for the processing fee for the actual permit, a year of "health insurance" and all of the copying and notarizing). After 3 years, he will be able to apply for long-term residence, since he is the father of Bulgarian children and living here with them. The long-term residence permit is a 1-time fee of 1000 bgn, but you have to renew the permit every 5 or so years (without paying the fee again).

Hope that helps. If you have specific questions, let me know. I moved here with my Bulgarian husband just over three years ago.

kojidae-
Thank you for all the information! We are still researching our options.  We will be in Bulgaria in the spring early summer, and it will be great if we can meet for a coffee or lunch.  I have family in Burgas and this will be our main place to stay.  We are planning to go to Sofia and also I have family in Kazanluk and planning to go there at some point.  May be we can visit Gabrovo too.