In this work, we consider bilayer biomembranes or surfactants made of two amphiphiles A and B . Under a variation of a suitable parameter, such as temperature or difference of lengths of hydrophobic chains, these systems undergo a phase separation from a homogeneous liquid-phase to two distinct liquid-phases. Two physical situations can be distinguished: (1) The amphiphiles A and B prefer to jump from a monolayer to the other ( flip-flop transition), (2) the mixture phase separates on each monolayer, and there is no jump from one sheet towards the second one ( lateral transition). To investigate the associated critical phase behavior, we first introduce a field theory, constructed with two order parameters (or fields) φ and ψ , which are nothing else but the composition fluctuations relative to the monolayers. Beside the usual terms proportional to φ 2 , ψ 2 , φ 4 and ψ 4 , the free energy contains an extra one, − C φ ψ , which describes the lowest order coupling between the two monolayers. The coupling constant C is positive for the lateral phase separation, and negative for the vertical one. We show that its sign results from a competition between the chemical segregation of amphiphiles and the curvature asymmetry. With the help of this free energy, we first identify the liquid-phases, and show the existence of a critical point, T c , of which the location depends naturally on the value of the coupling constant C . In particular, for those bilayer biomembranes or surfactants made of amphiphiles of the same chemical nature but with different lengths, and at fixed temperature, we show the existence of a critical line in the ( Δ c 0 , Δ l ) -plane, along which the bilayer undergoes a phase separation. Here, Δ c 0 and Δ l account for the curvature gap and the length difference, respectively. Second, we determine the behavior of the composition fluctuations, φ and ψ , and the total one, Φ = φ + ψ , upon temperature, T , and chemical potential difference, Δ μ , in the critical region. Third, we determine the critical behavior of the partial compressibilities, κ φ φ , κ ψ ψ and κ φ ψ , and the overall one, κ tot = κ φ φ + κ ψ ψ + 2 κ φ ψ . Finally, we remark that the flip-flop phase separation shows some analogy with the classical para-ferrimagnetic transition of coupled paramagnetic materials of Curie–Weiss type.