It has been shown previously that measurements of tides on Jupiter's moon Europa can be used to determine whether there is a liquid ocean beneath this moon's icy outer shell. In this paper we examine the further possibility of constraining the thickness of the icy shell in the case where a liquid ocean exists, by combining measurements of tidal gravity obtained from tracking an orbiting spacecraft with measurements of vertical tidal surface displacements obtained from a precise onboard altimeter. By simulating a 1-month Europa mapping mission we demonstrate that this combination of tidal measurements would provide a much better estimate of ice thickness than could be obtained using either tracking or altimeter measurements alone. The thickness value inferred from the combined data would also require an estimate of the shear modulus of Europa's icy shell. This introduces an additional uncertainty in the thickness estimate that is approximately proportional to the uncertainty in the inverse of the shear modulus.