  For $K$ an imaginary quadratic field with discriminant $-D_K$ and associated
quadratic Galois character $\chi_K$, Kojima, Gritsenko and Krieg studied a
Hermitian Maass lift of elliptic modular cusp forms of level $D_K$ and
nebentypus $\chi_K$ via Hermitian Jacobi forms to Hermitian modular forms of
level one for the unitary group $U(2,2)$ split over $K$. We generalize this
(under certain conditions on $K$ and $p$) to the case of $p$-oldforms of level
$pD_K$ and character $\chi_K$. To do this, we define an appropriate Hermitian
Maass space for general level and prove that it is isomorphic to the space of
special Hermitian Jacobi forms. We then show how to adapt this construction to
lift a Hida family of modular forms to a $p$-adic analytic family of
automorphic forms in the Maass space of level $p$.
