We analyze nonequilibrium lattice models with up-down symmetry and two absorbing states by mean-field approximations and numerical simulations in two and three dimensions. The phase diagram displays three phases: paramagnetic, ferromagnetic and absorbing. The transition line between the first two phases belongs to the Ising universality class and between the last two, to the direct percolation universality class. The two lines meet at the point describing the voter model and the size $ell$ of the ferromagnetic phase vanishes with the distance $varepsilon$ to the voter point as $ellsimvarepsilon$, with possible logarithm corrections in two dimensions.
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