Over the last two decades, integrated whispering-gallery-mode resonators have been increasingly used as the basic building blocks for selective filters, high-sensitivity sensors, and as nonlinear converters. In the latter two cases, optimum performance is achieved when the intra-cavity power or the resonance feature contrast are maximum. For devices with transversely singlemode resonator and access waveguides, the above-mentioned conditions are obtained when the system is critically coupled i.e. when the coupler power transfer rate corresponds to the single-pass intra-cavity loss. Designing coupled resonators for which critical-coupling is maintained over a large spectral range is therefore attractive to facilitate sensing or nonlinear frequency conversion. In this paper, we theoretically show, using a generic model based on the universal description of the device spectral characteristics and a coupled-mode theory treatment of the coupling section, that access-waveguide-coupled resonators can exhibit a wideband critical-coupling bandwidth when their constitutive resonator and access waveguides are different i.e. when they are phase-mismatched. To illustrate this, we have calculated the spectral response of Si3N4/SiO2 racetrack resonators and have found that, when the coupler beat-length becomes achromatic, the device critical-coupling bandwidth is expanded by more one order of magnitude compared to their phase-matched counterpart.