You can generally paint indoors even if it's raining outside. Just make sure the humidity inside is under 70 percent for best results.
During periods of heavy rain outdoors the air inside can become more humid than normal as well. Humidity is paint's enemy; excessive moisture can cause longer drying times or make the paint fail completely. Use a hygrometer to test the relative humidity inside your home, and employ a dehumidifier to remove excess moisture if necessary. Ideal painting conditions, inside or out, are humidity levels of 40 to 60 percent and temperatures of between 60 and 85 degrees. For best results check the paint manufacturer's specifications.