We propose a new kind of optical spatial solitons in biased photovoltaic-photorefractive materials when the self-trapping beam couples coherently with a pump beam by codirectional degenerate two-wave mixing. Such solitons are a result of double balance, i.e., loss is balanced by gain provided by the pump beam via two-wave mixing, and diffraction is balanced by nonlinearity that is due to the spatially nonuniform screening of the applied field, the photovoltaic effect, and the periodic modulation of the refractive index via two-wave mixing. These solitons possess some unique properties, are stable relative to small perturbations, and can become screening-photovoltaic solitons if the pump beam is switched to a background illumination.