Larry- check to see if your digital camera has a setting for white balance. Florecent , incandescent , and daylight all have different color temperatures, measured in degrees Kelvin. Flash and daylight are about the same. Mixed lighting sources is where you are getting in trouble.
Film is the same way. Did you ever shoot Ektachrome film indoors and notice that the color doesn't look right? Its color or white balance is for daylight or about 5500 degrees kelvin, if I remember correctly. That's why everything has a green cast.