A theory is presented to investigate the existence of incoherent coupled soliton family supported by two-photon isomerization nonlinearity. It is found that incoherent coupled gray and dark soliton families can exist in bulk polymers with the two-photon isomerization(TPI) nonlinearity. These soliton families can be established provided that their components have the same polarization and wavelength, and are mutually incoherent. The existing conditions and properties of this kind of incoherent coupled gray and dark soliton families are investigated in detail by numerical method. Each component of an incoherent coupled soliton family has the same full width of half maximum. When this incoherent coupled gray or dark soliton family propagates together, all the components can propagate stably in the polymers with two-photon isomerization nonlinearity. The investigation shows that the components of a gray soliton family have a transverse velocity, while those of dark soliton family don’t move in the transverse direction. If there are only two components, incoherent coupled TPI soliton families automatically degenerates to incoherent coupled TPI gray or dark soliton pairs.