We studied salt-free, highly concentrated (5-200 g/L) mixtures of unfragmented (mum contour length) DNA and hyaluronic acid (HA) as a borderline example of rigid-rod/flexible-chain composite, across a broad range of concentration ratios c(HA)/c(DNA) = 0.05-50. By polarizing microscopy, we established that the DNA and HA form clearly separated thread-like domains defined and oriented by solution shear. Within its domains, DNA shows birefringent banded patterns, routinely observed for long chain mesogens. We applied small-angle X-ray scattering (SAXS) to the mixtures and observed a polyelectrolyte (PE) correlation peak at q*wave vector. This peak was ascribed to DNA subphase and was used as a measure of the effective DNA concentration in the subphase c*(DNA), according to deGennes scaling relationship between the DNA mesh size xi = 2 pi/q*alpha c(-1/2) and monomer concentration c. From c*(DNA) (and initial c(HA) and c(DNA)), we inferred the effective c(HA)* of HA subphase. We find a concentration-independent ratio Gamma = c*(HA)/ c*(DNA) approximate to 0.85 across a broad range of 0.02-0.4 M. As there is the osmotic pressure (Pi) equilibrium between DNA and HA subphases, the constant G indicates that Pi alpha c(9/8) scaling common for DNA and other highly charged PEs is valid also for HA (a weak PEdoes not feature counterion condensation). Therefore, we propose that this deviation from the conventional osmotic pressure scaling Pi alpha c cannot originate from the concentration dependence of counterion condensation, which is an implicit but common interpretation in the literature. Further, as HA releases all its counterions into the solution, the HA osmotic coefficient phi(HA) we took as a measure of the DNA osmotic coefficient which we found to be phi(DNA) approximate to 0.28. This, double the Manning value, corroborates a result by Raspaud et al.