NIntegrate with variable in it

I would like to NIntegrate with a variable in the function. Later I will be series expanding it. Can it be done in Matehematica? I am getting errors for a sample integration as,

NIntegrate[Series[Cosh[x]*Exp[-z*Cosh[x]], {z, 0, 2}], {x, 0, \[Infinity]}]

The error is,

NIntegrate::inumr: The integrand Cosh[x]-Cosh[x]^2 z+1/2 Cosh[x]^3 z^2+O[z]^3 has evaluated to non-numerical values for all sampling points in the region with boundaries {{\[Infinity],0.}}.

Is there a way out? I know that, analytically, I can obtain expressions in terms of modified Bessel functions of second kind. But Mathematica does not pick that up.