We examine the interplay between ferromagnetism and superconductivity in bilayer and trilayer heterostructures based on Co, YBa2Cu3O7-delta (YBCO), and La0.7Ca0.3MnO3 (LCMO) thin films grown on SrTiO3 substrates with typical thicknesses of 10-15 nm. We have measured magnetoresistance below the resistive-superconducting onset of the YBCO. Naturally oxidized antiferromagnetic CoO top layer films give rise to pronounced exchange bias, modifying the coercive field of the Co by several hundred Oe. This allows separating effects at coercivity, such as stray fields, from those of parallel vs. antiparallel magnetic alignment between top and bottom ferromagnetic layers. In bilayers of Co/YBCO and of LCMO/YBCO, we observe a small magnetoresistance peak centered at the coercive field of the ferromagnetic layer of at most 20%, which we attribute to the effect of stray fields generated in the domain state of the ferromagnet. In the case of the CoO/Co/YBCO/LCMO/SrTiO3 trilayer, aside from the peaks at coercivity, we observe a well-defined plateau of the magnetoresistance extending between the coercive fields of the LCMO and Co, with a width that is modified by the exchange-biased Co layer. Reactivity between Co and YBCO at the interface gives rise to a progressive deterioration in the superconducting transition temperature. Aged samples display magnetoresistance peaks at the coercive fields of the Co and LCMO characteristic of stray fields without the magnetoresistance plateau between them.