Thermodynamic properties of a system of interacting bosonic particles and antiparticles at finite temperatures are studied within the framework of a thermodynamically consistent mean field model. The mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. We assume a conservation of the isospin density for all temperatures. It is shown that, independently of the strength of the attractive mean field, at the critical temperature $T_c$ the system undergoes the phase transition of second order to the Bose-Einstein condensate, which exists in the temperature interval $0 le T le T_c$. It is obtained that the condensation represents a discontinuity of the derivative of the specific heat at $T = T_c$ and condensate occurs only for the component that has a higher particle-number density in the particle-antiparticle system.
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