I would be careful in asking this as an "R linear regression" question versus a "linear regression" question. Formulas is R have rules that you may or may not be aware of. For example:
http://wiener.math.csi.cuny.edu/st/stRmanual/ModelFormula.html
Assuming you're asking if the following equation is linear:
a = coeff0 + (coeff1 * b) + (coeff2 * c) + (coeff3 * (b*c))
The answer is yes, if you assemble a new independent variable such as:
newv = b * c
Substituting the above newv equation into the original equation probably looks like what you're expecting for a linear equation:
a = coeff0 + (coeff1 * b) + (coeff2 * c) + (coeff3 * newv)
As far as references go, Google "r regression", or whatever you think might work for you.