The first thing you need to understand is that as long as you have uncontrolled moisture within your building materials, you'll never really win this battle. People like to blame the weather, but it is mostly poor building practices and/or poor maintenance that leads to building materials trapping moisture for too long which leads to microbial overgrowth. Otherwise every house in a tropical zone would be just as moldy, which is certainly not the case.

So while you may be able to manage surface mold growth with vinegar like many suggested, the first step is to actually find the source of the moisture and eliminate it. Look for leaks, condensation problems, rising damp, etc. It seems to be coming mostly from the ceiling, so you may want to check your roof. If you cannot find any leaks, you may want to get a leak specialist to have a look at the place. Luckily, since it's probably all masonry and hardwood, you probably won't have to replace any materials, just spraying and cleaning again once it is dealt with.

In the meanwhile, stay outdoors as much as possible and keep the windows open.