This paper tackles the problem of joint users' uplink transmission power and data rate allocation in multi-service two-tier femtocell networks. Each user-either macrocell (MUE) or femtocell user equipment (FUE)-is associated with a two-variable utility function that represents his perceived satisfaction with respect to his allocated resources (i.e., power and rate). User's utility function is differentiated based both on the tier that the user belongs to and the service he requests. The joint resource allocation problem is directly confronted as a two-variable optimization problem and formulated as a non-cooperative game. The theory of supermodular games is utilized towards treating the two-variable optimization problem and the inherent multidimensional competition that arises among the users. The existence of proposed game's Nash Equilibrium (NE) point is analytically shown, while game's convergence to its NE point is proven. A distributed and iterative algorithm for computing the desired NE is introduced, where the optimal values of each user's uplink transmission power and data rate are simultaneously updated at the same step. The performance of the proposed approach is evaluated via modeling and simulation and its superiority compared to other state of the art approaches is illustrated.