Very large values of magnetocapacitance originated from the coupling of magnetic and dielectric properties were observed in La0.7Ca0.3MnO3/BaTiO3 superlattices (SL). The SL of composition [LCMO25/BTO20]10 was deposited on MgO(100) substrates by the metal organic aerosol deposition technique. The formation of SL was evident from the X-ray diffraction pattern shown typical satellite peaks arising from the artificial SL periodicity. High resolution TEM images demonstrate coherent strained SLs with in plane lattice parameter equal to first LCMO layer that was grown unstrained on MgO(100). Magnetic properties of the SL grown on MgO(100) substrate were peculiar to those of very thin LCMO films, i.e. the saturated magnetic moment MS and the Curie temperature TC=220K were reduced and the ferromagnetic transition was broadened. The magnetocapacitance, MC(H)=100%×[C(H)–С(0)]/C(0), at μ0H=7T was 14% at 10K and 800% at the metal-insulator transition temperature TMI =180K. The analysis in terms of an equivalent circuit revealed that the majority of this effect originated from the colossal magnetoresistance (CMR), which generally reached maximum value at TMI in LCMO layers. The CMR effect was as large as 2600% at TMI, but it was very small <1% at 10K and at this low temperature the magnetocapacitance effect can be resulted from magnetoelectric coupling between LCMO and BTO layers. The reason for the magnetoelectric coupling is the elastic coupling of the piezoelectric BTO and magnetostrictive LCMO layers in the SL. Effective elastic coupling was not limited by clamping of the LCMO/BTO SL to the substrate due to incommensurate growth of the first LCMO layer on a large >8% mismatched MgO(100) substrate.