  We construct exactly solved commuting projector Hamiltonian lattice models
for all known 2+1d fermionic symmetry protected topological phases (SPTs) with
on-site unitary symmetry group $G_f = G \times \mathbb{Z}_2^f$, where $G$ is
finite and $\mathbb{Z}_2^f$ is the fermion parity symmetry. In particular, our
models transcend the class of group supercohomology models, which realize some,
but not all, fermionic SPTs in 2+1d. A natural ingredient in our construction
is a discrete form of the spin structure of the 2d spatial surface $M$ on which
our model is defined, namely a `Kasteleyn' orientation of a certain graph
associated with the lattice. As a special case, our construction yields
commuting projector models for all $8$ members of the $\mathbb{Z}_8$
classification of 2d fermionic SPTs with $G = \mathbb{Z}_2$.
