We address nonlocal nonlinear solitons in a lattice consisting of two different semi-infinite periodic lattices imprinted in a nonlocal nonlinear medium. We study in detail the existence and stability of these solitons using bandgap structures. We discover that surface solitons are unstable when modulation has a step on the heterointerface of two different semi-infinite periodic lattices, and there are different types of solitons for “no modulation step” when the input beam exists at different positions.