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Here, we discuss a model for the quasi-static magnetoelectric (ME) interaction in three-layer composites consisting of a single piezoelectric (PE) layer and two magnetostrictive (MS) layers with positive and negative magnetostriction. Two types of layer arrangements are considered: Type 1: a sandwich structure with the PE layer between the two MS layers and Type 2: the two MS layers form the adjacent layers. Expressions for the ME response are obtained using the system of equations of elasto- and electrostatics for the PE and MS phases. The contributions from longitudinal and bending vibrations to the net ME response are considered. The theory is applied for trilayers consisting of lead zirconate titanate (PZT), nickel for negative magnetostriction, and Metglas for positive magnetostriction. Estimates of the dependence of the strength of the ME response on the thickness of the three layers are provided. It is shown that the asymmetric three-layer structures of both types lead to an increase in the strength of ME interactions by almost an order of magnitude compared to a two-layer piezoelectric-magnetostrictive structure. The model predicts a much stronger ME response in Type 2 structures than in Type 1. The theory discussed here is of importance for designing composites for applications such as magnetic field sensors, gyrators, and energy harvesters.