My husband says the darker the exterior paint is the hotter the interior of the home is in the summer is this true?

I'm not a housing expert but here's my scientific viewpoint -

Dark colours do absorb more light energy. They look dark because less light is reflected. However I would doubt that this would be sufficient to cause a raise in interior home temperature unless the walls were not very well insulated. Insulation keeping warm out as well as cold. It's an interesting theory but my money would be on no.

Second thoughts - remembered someone telling me houses are whitewashed in hot countries to help keep them cool so maybe with thin enough walls it can make a difference.
Really want to carry out an experimant now...

I'd say the effect would be dependent on the surface area of the house, the light intensity and colour absorbance vs the insulation properties of the walls in question.

Sorry to witter at you this question just really interested me!

I believe the effect on the interior temperature would be determined by the insulation in the walls (may be a longer retention of the day's heat, after the sun sets, on or in the wall by darker color) but the temperature around the outside of the house may be even more effected by the lighter or darker color choice.. I'd guess... hotter in the yard with light color and less radiant heat with darker color.