The achievable bandwidth in ladder acoustic filters is strictly limited by the electromechanical coupling coefficient (k;) in conventional ladder-acoustic filters. Furthermore, their out-of-band rejection is inherently weak due to the frequency responses of the shunt or series-connected acoustic resonators. This work proposes a coupling-matrix-based solution for both issues by employing acoustic and electromagnetic resonators within the same filter prototype using prescribed Chebyshev responses. It has been shown that significantly much wider bandwidths, that cannot be achieved with acoustic-only filters, can be obtained. An important strength of the proposed method is that a filter with a particular FBW can be designed with a wide range of acoustic resonators with different k; values. An 14 % third-order asymmetrical-response filter is designed and fabricated using electromagnetic resonators and an acoustic resonator with a k; of 3.5 %.