If you are using latex acrylic paint you need at least two hours of sun for paint to dry before the rain comes.  If heavy rain is forecast or several days of rain are coming in the next few days, you will need about six hours of good sun to dry the paint thoroughly enough to not be affected.  Paint will dry to the touch in one hour or so depending on the heat of the day.  It takes about five days of normal weather for paint to dry all the way through and for the paint film to reach its maximum hardness and durability.

If it rains before the paint surfaces dry the rain will wash some of the paint off that were painted last.  This is rarely a problem because the surfaces, when dry the next day, can just be repainted.

Exceptions to this rule would be if you are using oil base pant.  Oil base takes longer to dry and therefore rain should not be in the forecast for about 24 hours.  Oil base paint is not recommended on exterior surfaces in southern climates.  The oil base paint weathers very quickly in a sunny climate and loses its gloss and does not have the flexibility it needs to endure the hot sun.  It will generally crack and peel much more readily then acrylic paint.  It is also begins to break down in three or four years and becomes very susceptible to mildew which feeds on the resins in the oil base paint.  It is subject to rapid color fade and chalking.

How soon can you paint a house after the rain?

Generally if the surface is dry to the touch you can paint the surface if using acrylic paint.  The acrylic paint allows small amounts of moisture to pass through the coating from the surface to the air.  It is a rare occurrence for acrylic paint to bubble due to moisture.

If using oil base, which is not recommended, you must have a perfectly dry surface which may take one or two good days of drying weather.