Complicated wounds often require specialized medical treatments, and hydrogels have emerged as a popular choice for wound dressings in such cases due to their unique properties and the ability to incorporate and release therapeutic agents. Our focus was to develop and characterize a new optimized formula for biohybrid hydrogel membranes, which combine natural and synthetic polymers, bioactive natural compounds, like collagen and hyaluronic acid, and pharmacologically active substances (doxycycline or npAg). Dynamic (oscillatory) rheometry confirmed the strong gel-like properties of the obtained hydrogel membranes. Samples containing low-dose DOXY showed a swelling index of 285.68 ± 6.99%, a degradation rate of 71.6 ± 0.91% at 20 h, and achieved a cumulative drug release of approximately 90% at pH 7.4 and 80% at pH 8.3 within 12 h. The addition of npAg influenced the physical properties of the hydrogel membranes. Furthermore, the samples containing DOXY demonstrated exceptional antimicrobial efficacy against seven selected bacterial strains commonly associated with wound infections and complications. Biocompatibility assessments revealed that the samples exhibited over 80% cell viability. However, the addition of smaller-sized nanoparticles led to decreased cellular viability. The obtained biohybrid hydrogel membranes show favorable properties that render them suitable for application as wound dressings.