We investigate the effect of polysoaps on the phase behavior and membrane elastic properties of the lyotropic lamellar (L-alpha) phase of the nonionic surfactant penta(ethylene glycol) dodecyl ether (C12E5). The polysoap is a hydrophobically modified polymer (hm-polymer) with n-alkyl side groups randomly grafted to a polyacrylate (PAA) backbone. The membrane properties are extracted from small-angle neutron scattering data based on a model developed by Nallet et al. and the excess area method developed by Roux et al. The phase behavior, membrane rigidity, compression modulus, and bilayer mean bending modulus are found to be independent of molecular weight, polydispersity, and hydrophobe length of hm-polymers. The rigidity and compression moduli of membranes increase with increasing polymer concentration and hydrophobe substitution level. A minimum hydrophobic interaction strength (combination of hydrophobe length and hydrophobe substitution level) is required to produce single phase polysoap/lamellar surfactant systems. A scaling model is proposed that defines the boundaries between homogeneous and biphasic solutions based on two criteria: (1) the surface coverage of chain segments between hydrophobus (i.e. blobs) must be less than the available membrane area and (2) the interlamellar spacing must be larger than the blob size. This simple model captures the essential features of the phase diagrams.