In the interstellar medium, carbon is distributed between the gas and solid phases. However, while about half of the expected carbon abundance can be accounted for in the gas phase, there is considerable uncertainty as to the amount incorporated in interstellar dust. The aliphatic component of the carbonaceous dust is of particular interest because it produces a significant 3.4 $��$m absorption feature when viewed against a background radiation source. The optical depth of the 3.4 $��$m absorption feature is related to the number of aliphatic carbon C-H bonds along the line of sight. It is possible to estimate the column density of carbon locked up in the aliphatic hydrocarbon component of interstellar dust from quantitative analysis of the 3.4 $��$m interstellar absorption feature providing that the absorption coefficient of aliphatic hydrocarbons incorporated in the interstellar dust is known. We generated laboratory analogues of interstellar dust by experimentally mimicking interstellar/circumstellar conditions. The resultant spectra of these dust analogues closely match those from astronomical observations. The measurements of the absorption coefficient of aliphatic hydrocarbons incorporated in the analogues were carried out by a procedure which combined FTIR and $^{13}$C NMR spectroscopies. The absorption coefficients obtained for both interstellar analogues were found to be in close agreement (4.76(8) $\times$ 10$^{-18}$ cm group$^{-1}$ and 4.69(14) $\times$ 10$^{-18}$ cm group$^{-1}$), less than half those obtained in studies using small aliphatic molecules. The results thus obtained permit direct calibration of the astronomical observations, providing rigorous estimates of the amount of aliphatic carbon in the interstellar medium.