The characteristics of magnetoelectric (ME) effects in planar composite ferromagnet-piezoelectric heterostructures strongly depend on the direction of magnetization of the heterostructure. These dependences affect the parameters of magnetic field sensors, energy harvesters, and electronic devices based on ME effects. In this work, the frequency and field characteristics of the direct ME effect in an obliquely-magnetized heterostructure containing a piezoceramic plate of lead zirconate titanate and a nickel layer electrolytically deposited on its surface were experimentally studied. The measurements were carried out at the resonant frequency of the structure ∼85 kHz under excitation with a weak harmonic field. When the dc magnetic field deviated from the plane of the structure, the resonance frequency remained unchanged, the value of the ME coefficient gradually decreased from 5.0 V/(Oe∙cm) to a minimum, and the range of operational magnetic fields expanded towards higher fields. The transformation of the ME effect characteristics occurred due to a change of the internal field in the ferromagnetic layer caused by demagnetization. A method allowing calculating the field characteristics of the ME effect in obliquely magnetized heterostructures was proposed. The results obtained can be used to control parameters of ME devices and design vector sensors of dc magnetic fields.