We derive a (2+1)-dimensional multicomponent long-wave-short-wave resonance interaction (LSRI) system as the evolution equation for propagation of N-dispersive waves in weak Kerr-type nonlinear medium in the small-amplitude limit. The mixed- (bright-dark) type soliton solutions of a particular (2+1)-dimensional multicomponent LSRI system, deduced from the general multicomponent higher-dimensional LSRI system, are obtained by applying the Hirota's bilinearization method. Particularly, we show that the solitons in the LSRI system with two short-wave components behave like scalar solitons. We point out that for an N-component LSRI system with N >3, if the bright solitons appear in at least two components, interesting collision behavior takes place, resulting in energy exchange among the bright solitons. However, the dark solitons undergo standard elastic collision accompanied by a position shift and a phase shift. Our analysis on the mixed bound solitons shows that the additional degree of freedom which arises due to the higher-dimensional nature of the system results in a wide range of parameters for which the soliton collision can take place.