New type of direct-coupled resonator filter with complementary couplings is analyzed and described. Complementary couplings are capacitive (electric) and inductive (magnetic) couplings used together in one filter. Capacitive and inductive effects complement each other in terms of frequency dependence. That is why complementary couplings filter behaves exactly like classical filter with ideal frequency independent couplings. The new type of filter gives strictly Chebyshev frequency response in wideband and ultra-wideband applications what is unique in other filter realizations. This phenomenon is explained by modeling direct-coupled resonator filters with real admittance inverters. A novel microstrip wideband filter with complementary couplings is proposed. The 5th order, 2.0 GHz center frequency and 600 MHz bandwidth example is presented.