  We study the thermodynamic behavior of attractive binary Bose mixtures using
exact path-integral Monte-Carlo methods. Our focus is on the regime of
interspecies interactions where the ground state is in a self-bound liquid
phase, stabilized by beyond mean-field effects. We calculate the isothermal
curves in the pressure vs density plane for different values of the attraction
strength and establish the extent of the coexistence region between liquid and
vapor using the Maxwell construction. Notably, within the coexistence region,
Bose-Einstein condensation occurs in a discontinuous way as the density jumps
from the normal gas to the superfluid liquid phase. Furthermore, we determine
the critical point where the line of first-order transition ends and
investigate the behavior of the density discontinuity in its vicinity. We also
point out that the density discontinuity at the transition could be observed in
experiments of mixtures in traps.
