Tire–road interaction addresses safety with respect to braking friction and energy efficiency in the context of rolling resistance. These phenomena are coherent, but their engineering solutions can be contradictory. For example, highly skid-resistant surfaces may not be ideal for fuel economy, but surfaces with low rolling resistance may be prone to skidding. Several experimental and numerical studies have investigated the individual phenomena, but insufficient attention has been paid to studying them coherently. The present study computed braking friction and rolling resistance for various operating parameters and their coherent response for each parameter with the use of a thermomechanical contact algorithm. Micromechanical finite element simulations of a rolling or braking pneumatic tire against selected asphalt concrete surfaces were performed for various operating conditions, such as tire load, inflation pressure, speed, and ambient air and pavement temperatures. The coefficients of braking friction and rolling resistance were found to decrease with the inflation pressure and the temperature and to increase with the wheel load. The braking friction coefficient was found to decrease with the speed, in contrast to the rolling resistance coefficient, which increases with the same parameter. A full-skidding tire registered lower braking friction than a 20% slipping tire. Also, an asphalt surface with higher macrotexture offered higher braking friction and higher rolling resistance, and vice versa.