We report the synthesis of a series of block copolymers tailored with phosphonic acid groups, poly(styrene phosphonate-b-methylbutylene) (PSP-b-PMB), which show systematic phase sequences of a disorder, lamellae, and hexagonal cylinder morphology, with controlled acid concentration. These observations were combined with the Leibler theory in order to estimate the effective Flory-Huggins interaction parameter of PSP-b-PMB, chi(PSP-PMB). For example, chi(PSP-PMB) = 0.101 + 13.823/T was anticipated for the disordered phases observed at the low phosphonation level of 15 mol %. The direct comparison of PSP-b-PMB block copolymers and their sulfonated analogues, poly(styrenesulfonate-b-methylbutylene) (PSS-b-PMB), revealed a remarkably similar phase behavior. In-depth thermodynamic studies suggested similar chi values regardless of the kind of acid group when the concentration is lower than 20 mol %, whereas these values vary by increasing the amount of acid groups, as polymers carrying phosphonic acid groups showed a weaker segregation strength. In order to provide insights into the design of acid-bearing polymers as advanced polymer electrolytes, their ion transport properties were investigated upon the addition of various ionic liquids (ILs). The introduction of alkyl substituents in the IL cations was found to be advantageous to improve the conductivity of IL-containing PSP-b-PMB membranes by inducing favorable thermodynamic interactions of the ILs with the polymer matrix, unlike the results observed for IL-containing sulfonated samples. These polymers have the potential to be alternatives to the widely studied sulfonated polymers.