Perovskite manganites are well known for their complex magnetic and electronic properties. Their heterostructures are even more perplexing, specifically when interfaced with magnetic or nonmagnetic insulators as they offer particular promise for applications such as spin filter tunnel junctions. This study explores the structural and magnetic properties of one such heterostructure, namely, La0.7Sr0.3MnO3/LaCoO3 (LSMO/LCO) bilayers as the thickness of the LCO layer is varied while keeping that of the LSMO layer fixed. Exceeding a threshold value while gradually increasing the LCO layer thickness, prominent side lobes are observed in the reciprocal space map signifying the formation of periodic structural striped domains in LCO. The magnetic properties of the bilayers, specifically the interfacial couplings, are markedly influenced by the variation of the LCO thickness with noteworthy consequences that include a tunable negative exchange bias.