Is there a word for a compound that has both ionic and covalent bonds?
There may be a strong case to call this a "salt", like other ionic compounds.  Very often, the anion (negative ion) of a salt is an ion comprised of different atoms with covalent bonds.  For example, $\ce{ SO_4^{2-} }$ is the sulfate anion, and the bonds between $\ce O$ and $\ce S$ are covalent to some degree.  So $\ce{ Na_2SO_4 }$ is an ionic compound under this definition.  Thus, any compound with some component that is strongly ionic can be called an ionic compound; i.e. a salt, regardless of the bonding structure of the components.