redshift - Estimating galactic dust extinction for medium band filters

The quantity you want is basically the extinction law, and is usually called $k(lambda)$. An extinction law is a fit to several measurements of the extinction $A_lambda$ in some direction (or an average of several directions).

Cardelli et al. (1989) provides different functional forms for the mean extinction law, parametrized in their Eq. 1 as
$$
frac{A_lambda}{A_V} = a(x) + frac{b(x)}{R_V},
$$
where $x$ is the inverse wavelength in $mumathrm{m}^{-1}$, and the coefficients are given separately for IR, optical, UV, and FUV in Eqs. 2, 3, 4, and 5, respectively. The total-to-selective extinction $R_Vequiv A_V/E(B-V)$ takes different values for different lines of sight, but usually lies in the range 2.5 to 6, with 3.1 being a typical value in the Milky Way.

To get the quantity you're interested in, simply convert your favorite wavelength to $x$, stick into Eq. 1, and multiply by $R_V$:
$$
k(lambda) equiv frac{A_lambda}{E(B-V)} = frac{A_lambda}{A_V} R_V.
$$