We study the joint unicast and multi-group multicast transmission in massive multiple-input-multiple-output (MIMO) systems. We consider a system model that accounts for channel estimation and pilot contamination, and derive achievable spectral efficiencies (SEs) for unicast and multicast user terminals (UTs), under maximum ratio transmission and zero-forcing precoding. For unicast transmission, our objective is to maximize the weighted sum SE of the unicast UTs, and for the multicast transmission, our objective is to maximize the minimum SE of the multicast UTs. These two objectives are coupled in a conflicting manner, due to their shared power resource. Therefore, we formulate a multiobjective optimization problem (MOOP) for the two conflicting objectives. We derive the Pareto boundary of the MOOP analytically. As each Pareto optimal point describes a particular efficient trade-off between the two objectives of the system, we determine the values of the system parameters (uplink training powers, downlink transmission powers, etc.) to achieve any desired Pareto optimal point. Moreover, we prove that the Pareto region is convex, hence the system should serve the unicast and multicast UTs at the same time-frequency resource. Finally, we validate our results using numerical simulations.