Perforated multilayer partitions are widely used in many problems for the aerospace and automotive industries and air-conditioning systems. Combinations of macro and micro-perforated perforations across the constitutive partition layers can provide different physical mechanisms for diverse control strategies depending on the problem requirements. However, there is a lack of unified numerical or analytical description able to provide accurate results over a broad frequency range for a wide range of diameter perforations ranging from supra-millimetric to sub-millimetric apertures. Furthermore, most of them do not account for the beneficial effects on the partition dissipation of the in-hole non-planar modes, albeit evanescent. In this work, an enhanced modal matching (EMM) method is presented that accounts for in-hole high-order modes as well as visco-thermal boundary layer effects inside the holes and over the outer surfaces surrounding the holes. The analytical results have been compared against effective models, numerical models and impedance tube measurements. They show good agreement for single and multi-layer partitions within the corresponding bandwidths of validity. Parametric studies have concluded that the panel thickness-to-hole diameter ratio is a key factor that plays a crucial role on the prominence of the in-hole radial modes and outer visco-thermal effects in the dissipation properties.