We present a new staggered discretization of the Dirac operator. Doubling gives only a doublet of Dirac fermions which we propose to interpret as a physical (lepton or quark) doublet. If coupled with gauge fields, an (1+g5) chiral interaction appears in a natural way. We define a generalization for curved background which does not require tetrad variables. The approach suggests a natural explanation for the three fermion families.