We consider a symmetrical poly(styrene-stat-(acrylic acid))-block-poly(acrylic acid), i.e., PSAA-b-PAA, diblock copolymer, with a molar fraction (phi(AA) = 0.42 of acrylic acid, in the more hydrophobic PSAA statistical first block. We investigate its structural behavior at constant concentration in water using small-angle neutron scattering (SANS) by varying (i) the ionization of its acrylic acid motives via the pH by adding NaOH and (ii) the ionic strength of the solution by increasing the NaCl salt concentration cs. We present the resulting morphological phase diagram (pH, cs), in which we identified two different lamellar phases presenting a smectic long-range order at small-to-intermediate ionizations and a spherical phase with a liquid-ike short-range order at larger ionization. In the low-ionization regime, the first lamellar phase comprises a water-free PSAA lamellar core surrounded by a dense poly(acrylic acid) brush swollen with water. Its mostly hydrophobic core still being glassy, this phase is unable, to reorganize and is frozen in. A detailed analysis of the SANS data shows the osmotic nature of the polyelectrolyte brush, in which the Na+ counterions are confined so that local electroneutrality is satisfied. Above the pH at which the PSAA statistical block starts ionizing, the PSAA lamellar core melts. The second lamellar phase identified then comprises a PSAA core thinner than that of the frozen-in previous phase, implying a significant increase of the core/water interface and a decrease of the brush surface density. The transition from the first lamellar phase to the second one can be quantitatively shown to result from the balance between the two contributions: (i) the extra interfacial cost between the thinner core and water and (ii) the associated gain in entropy of mixing for the counterions confined inside the brush. At even higher ionization, the diblocks finally form spherical objects with a very small, pH-dependent aggregation number and reach an apparent onset of self-association. When the highest ionization investigated is reached, the cores of these final spherical core-shell objects are found to contain a significant amount of water. We thereby demonstrate that at constant concentration, pH, and ionic strength both trigger a transition from frozen to molten hydrophobic phases as well as unexpected morphological transitions.