We consider the nonlinear propagation of bulk polaritons in a magnetically saturated ferromagnetic thick film, the applied magnetic field being perpendicular to the film plane. A (2+1)-dimensional asymptotic model equation generalizing the sine-Gordon one is derived. Line-soliton solutions are exhibited, their stability condition is derived. When unstable, line solitons decay into stable two-dimensional lumps, which are studied by means of variational analysis.