Precious metals such as palladium (Pd) and platinum (Pt) are marvelous materials in the fields of electronic and catalysis, but they are tapering day by day. Zr(IV)-based metal-organic frameworks (MOFs) are competent for their recovery, notably in harsh environments, while the general powder form limits their practical application. Porous MOF-based membranes with ultraefficient metal ion permeation, strong stability, and high selectivity are, therefore, strikingly preferred. Herein, a set of polymeric fibrous membranes incorporated with the UiO-66 series are fabricated; their adsorption/desorption capabilities toward Pd(II) and Pt(IV) are evaluated from strongly acidic solutions; and the MOF-polymer compatibilities are investigated. Polyurethane (PU)/UiO-66-NH2 showed strong acid resistance and high chemical stability, which are attributable to strong pi-pi interactions between PU and MOF nanoparticles with a high configuration of energy. The as-fabricated MOF membranes show extremely good adsorption/desorption performances without ruptures/coalitions of nanofibers or leak of MOF nanoparticles, and successfully display the efficacy in a gravity-driven or even continuous-flow system with good recycle performance and selectivity. The as-fabricated MOF membranes set an example of potential MOF-polymer compatibility for practical applications.