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A model of a mixture of spinless fermions and spin-zero hardcore bosons, with filling fractions ρ_{F} and ρ_{B}, respectively, on a two-dimensional square lattice with composite hopping t is presented. In this model, hopping swaps the locations of a fermion and a boson at nearest-neighbor sites. When ρ_{F}+ρ_{B}=1, the fermion hopping amplitude ϕ and boson superfluid amplitude ψ are calculated in the ground state within a mean-field approximation. The Fermi sector is insulating (ϕ=0) and the Bose sector is normal (ψ=0) for 0≤ρ_{F}<ρ_{c}. The model has coupled first-order transitions at ρ_{F}=ρ_{c}≃0.3, where both ϕ and ψ are discontinuous. The Fermi sector is metallic (ϕ>0) and the Bose sector is superfluid (ψ>0) for ρ_{c}<ρ_{F}<1. At ρ_{F}=1/2, fermion density of states ρ has a van Hove singularity, the bulk modulus κ displays a cusplike singularity, the system has a density wave (DW) order, and ϕ and ψ are maximum. At ρ_{F}=ρ_{κ}≃0.81, κ vanishes, becoming negative for ρ_{κ}<ρ_{F}<1. The evolution of fermion effective mass, Fermi band dispersions, and Fermi surfaces as a function of ρ_{F} is highlighted. The obtained value for the ratio of the estimated superfluid T_{c} to the fermion bandwidth, of approximately 0.12, agrees closely with reported values of the ratio for a variety of unconventional superfluids and superconductors with T_{c} values spread over nine orders of magnitude.