  We construct four-variable $p$-adic $L$-functions for cuspidal Hida families
on ${\rm GSp}(4)\times{\rm GL}(2)$ and prove a complete interpolation formula.
The archimedean zeta integrals are computed by using a partial interpolation
formula for the four-variable $p$-adic $L$-functions and some previously
constructed $p$-adic $L$-functions.
