The answer is that they are inclined by 60.2 degrees. Here's how you get this:
The celestial coordinates of the pole of the ecliptic are
(alpha1, delta1) = (18 hours, 90-23.4393 degrees)
= (270 degrees, 66.6 degrees)
The number 23.4393 is the inclination of the earth's axis to the ecliptic (also called "the obliquity of the ecliptic").
According the the Observer's Handbook, the celestial coordinates of the north pole of the Milky Way are
(alpha2, delta2) = (12 h 51 m, 27 deg 8 min)
=(192.8 degrees, 27.1 degrees)
To calculate the inclination between the ecliptic and the Milky Way disk (i.e., the galactic plane), we need to calculate the distance between the ecliptic pole and galactic pole. This is done with the following spherical-trigonometry formula for the angle between two points on a sphere:
angle = arccos (sin (delta1) * sin (delta2) + cos (delta1) * cos (delta2) * cos (alpha1-alpha2))
If you plug in the above numbers, you get
angle = 60.2 degrees
This is the inclination between the ecliptic and the galactic plane.