Magnetoelectric (magnetic/piezoelectric) heterostructures bring new functionalities to develop novel transducer devices such as (wireless) sensors or energy harvesters and thus have been attracting research interest in the last years. We have studied the magnetoelectric coupling between Metglas films (2826 MB) and poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) in a laminate structure. The metallic Metglas film itself served as bottom electrode and as top electrode we used an electrically conductive polymer, poly(3,4-ethylene-dioxythiophene):poly(styrene sulfonate) (PEDOT:PSS). Besides a direct electrical wiring via a graphite ink, a novel contactless readout method is presented using a capacitive coupling between the PEDOT:PSS layer and an electrode not in contact with the PEDOT:PSS layer. From the experimental result we determined a magnetoelectric coupling of 1445 V/(cm·Oe) at the magnetoelastic resonance of the structure, which is among the highest reported values for laminate structures of a magnetostrictive and a piezoelectric polymer layer. With the noncontact readout method, a magnetoelectric coupling of about 950 V/(cm·Oe) could be achieved, which surpasses previously reported values for the case of direct sample contacting. 2D laser Doppler vibrometer measurements in combination with FE simulations were applied to reveal the complex vibration pattern resulting in the strong resonant response.