The method of membrane extraction for rare earth elements (REE) using the carrier N, N’-bisdioctylphosphorylmethyl-1,4-diaminobutane (DPDA-8) ions, leveraging an active transport mechanism, has been optimized. The distribution of DPDA-8 within the membrane pores was confirmed using scanning electron microscopy (SEM). Both light and heavy REE extractions from a simulated solution using DPDA-8 and trioctylphosphine oxide (TOPO) in 1,2-dichlorobenzene were explored. The influence of feed solution pH, carrier and anion concentration, supported liquid membrane (SLM) type and stability, and cell temperature, among other parameters, were meticulously examined. The results indicate a decrease in permeability with a decrease in feed solution pH attributed to competitive acid transport through the membrane. Additionally, the formation of H-complexes between carriers and perchloric or phosphoric acids was investigated using Fourier Transform Infrared (FTIR) spectroscopy and X-ray diffraction (XRD) techniques. Changes in the stretching bands of amino and phosphine oxide groups in DPDA-8 were monitored and characterized. XRD analysis of the crystal structures of salts DPDA-6·ClO4 and DPDA-12·H2PO4 revealed a two-dimensional layered supramolecular organization with varying anion positions relative to hydrophobic fragments. The DPDA-8 carrier demonstrated significantly higher permeability values compared to TOPO, with differences in permeability exceeding twofold for certain metals. FTIR spectroscopy identified the main coordination centers of DPDA-8 during the liquid–liquid extraction of specific REEs.