My husband has developed knots on the soles of his feet, and several hard white callous like growths on his palms. What could be going on?

May be corns, warts. A person with firm bumps on the soles most commonly has corns or warts. Corns are thickened skin areas, but warts are thickened areas with distorted "fingerprint" lines due to virus infection of the skin cells. A dermatologist or primary doctor should evaluate. On the palms, calluses (which are similar to corns) form if a person is getting pressure or friction repeatedly on certain palmar areas.
Fibroma. He may be developing a fibroma and needs to see his medical doctor since it is developing on his hands and feet.
Many possibilites. Many things can cause calluses. Some reasons that one may develop a callus include: viral infections (warts), friction, pressure, repedetive trauma, and a limitation of joint motion. Some genetic conditions may also cause people to develop calluses on the hands and the feet. Treatment depends on the cause of the problem. Have it evaluated by a professional and get the appropriate treatment.