He 111P - upgraded to Daimler-Benz DB 601 engines.
He 111H - more widely produced during World War II. DB 601 engines were changed to Junkers Jumo 211 engines. When the Jumo was fitted to the P model it became He 111 H.
He 111 H-2 - with Jumo 211A-1 engines, was fitted with improved armament. Two D Stands (waist guns) in the fuselage.
He 111 H-3 - Similar to H-2, but with Jumo 211 A-3 engines. The number of machine guns could be increased to seven with some variants having a belt-fed MG 17 installed in the tail. An MG FF cannon would sometimes be installed in the nose or front gondola.
He 111 H-16 - Fitted with Jumo 211 F-2 engines and increased defensive armament of MG 131 machine guns, twin MG 81Zs, and an MG FF cannon. (Late 1942)