Propagation of microwaves is studied in a composite material containing flakes of Fe-Si-Nb-Cu-B alloy placed into an epoxyamine matrix. The theory is worked out, which permits to calculate the coefficients of the dynamic magnetic permeability tensor and the effective magnetic permeability of the transversely magnetized composite. The measurements of magnetic field dependences of the transmission and reflection coefficients were carried out at frequencies from 12 to 38 GHz. Comparison between calculated and measured coefficients were conducted, which show that the calculation reproduces all main features of the resonance variations caused by ferromagnetic resonance and antiresonance. The dissipation of microwave power was calculated and measured. It is shown that the penetration depth of the electromagnetic field increases under antiresonance condition and decreases under resonance.