"Hand Full of Peter" is a band started by Lois and Peter Griffin where Peter played the guitar and Lois the mandolin. The band was first formed in the 1970s. Though the band members later became husband and wife, life became too busy, so the band was put on hold. The band got "back together" in the episode "Deep Throats" for a local talent show. Their songs include "Noble Indian Chief" and "A Lot of Tubes". They also thought they produced a song called "(In God's Eyes) Everybody's Hot", but it turns out they were so high on marijuana that they were just screaming "Aaaaahhh, Aaaaahhhhhh".
When Seth MacFarlane and Alex Borstein were on Inside the Actor's Studio with James Lipton, they alternately called "Hand Full of Peter" "Mouth Full of Peter", having failed to remember the exact title.