  The envelope function method traditionally employs a single basis set which,
in practice, relates to a single material because the $k\cdot p$ matrix
elements are generally only known in a particular basis. In this work, we
defined a basis function transformation to alleviate this restriction. The
transformation is completely described by the known inter-band momentum matrix
elements. The resulting envelope function equation can solve the electronic
structure in lattice matched heterostructures without resorting to boundary
conditions at the interface between materials, while all unit-cell averaged
observables can be calculated as with the standard envelope function formalism.
In the case of two coupled bands, this heterostructure formalism is equivalent
to the standard formalism while taking position dependent matrix elements.
