The biophysical characteristics of cell adhesion from single protein to cell length scales have primarily been studied using purely elastic substrates. However, natural extracellular matrix (ECM) is viscoelastic and contains mobile components. In this work, we combined chemistry and cell biology tools to design and characterize laterally mobile viscoelastic polymer films that promote receptor-specific cell adhesion. Moreover, we used amphiphilic block copolymers that are end-labeled with RGD peptide ligands to allow for integrin-mediated cell adhesion. The addition of a trace hydrophobic homopolymer in the supported bilayer block-copolymer films is used to tune the lateral mobility of the films. NIH 3T3 fibroblasts demonstrate a non-linear spreading response against the mobility of the RGD-displaying polymer films. Employing immunostaining and adhesion strength assays, we decoupled the partial contributions of focal adhesions (FA) and integrin-RGD complexes on cell adhesion. Furthermore, we employed these biomimetic polymer platforms to investigate the importance of viscous dissipation within the extracellular substrate and its connection to cell-surface receptors. Our results suggest that cells preferentially use avb3 and a5b1 integrins to control spreading and polarization in response to mechanical properties of their substrate. In order to further control the spatial presentation of biochemical molecules on mechanically-tunable polymer substrates, we successfully transferred fibronectin patterns on bilayer polymer films. We showed that NIH 3T3 fibroblasts spreading and adhesion features depend on the mechanical properties of these hybrid materials even in the presence of spatially and chemically identical biochemical signals. Overall, the present work demonstrates the potential of amphiphilic block copolymers to form artificial substrates that can capture a key feature of cell-ECM interactions: specifically, the ability of cells to induce changes in the substrate over time. Furthermore, it highlights the need for future studies on cell-substrate interactions that simultaneously consider the time-dependent mechanical properties of the ECM, the spatial characteristics of ligand presentation, and the receptor-mediated intracellular signaling.