I live in New Jersey,  I am in the process of re-modeling my house.  I am currently working upstairs and have the walls exposed.  This house is a red brick cape with double layered brick, built in 1954.  There is no gap between the two layers of brick, the layers of brick are back to back.  This house has no insulation in the walls,  two layers of old style sheet rock that looks like this
https://www.dropbox.com/s/uzvg0fjgn...4.jpg?dl=0

Which is covered by a layer of wood paneling.  There is probably a 2 inch gap between the old sheet rock and the brick.  I can't tell how the walls are framed against the brick because I have not demoed a wall downstairs yet.   Are these brick  walls  safe to be insulated inside?  If so, what process should be followed?  I am concerned after reading many articles about how brick walls should not be insulated due to moisture issues....

I did expose the upstairs walls.  I would like to get the upstairs finished first then move down stairs.  I have two walls of brick upstairs  and I am unsure on how to proceed in regards to insulating these walls.  Here are some pictures...  https://www.dropbox.com/sh/fhucimdw...iwz6a?dl=0

the "old sheetrock" is called "rock lath" and is still available as a plaster base. You're right that insulating masonry walls is problematic, so do your research. There are lots of articles on this site: http://www.greenbuildingadvisor.com/search/node/insulating%20brick%20houses that address the issue. (I used "insulating brick houses" in the search box). Also, try this site which will have lots and lots of information: http://buildingscience.com.

Double brick houses are very common in Europe....

My contractor just found these questions and suggested I respond. I have just been through a major rebuild of a 1929 home with very similar construction, used magboard throughout. The problems of insulating inside a brick building are quite unique -- and challenging, mostly because of condensation issues. If you are still wanting a response to your questions and are not too far along already, please say so, and I'll share what we have learned. Otherwise I won't bother.

If you're going to seriously re-insulate, and aren't going to resheath the outside, you're going to be reframing the exterior walls (at least) on the inside to create a gap for insulation.

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It's possible to get to IRC 2015 code minimum on U-factor basis reasonably safely with 1/2" of air gap between the brick layer and 2.5" of continuous rigid foil faced polyisocyanurate (R15-ish), seams taped and sealed, strapped to the brick with 1x4 furring through-screwed to the brick with masonry screws, onto which the wallboard gets mounted. There has to be some careful detailing of window & door flashing, and anywhere joists & rafters are resting on or embedded brick (with perhaps a bit of 2lb polyurethane in those areas). It may or may not be necessary to create weep holes or vents near the top & bottom of the brick cavity, but you DO want the brick to be able to dry in both directions if you can, to limit the risk of freeze/thaw spalling. Deep roof overhangs that limit exterior wetting can help lower that risk, so some amount of assessment needs to be made first.

Some houses with large roof overhangs, good drainage and ocean-moderated outdoor temperatures can even be safely done with rock wool or cellulose directly in contact with the brick, still others with 2-3" of HFO-blown 2lb polyurethane spray foam. Got a ZIP code? Some parts of NJ are US zone 5A, others zone 4A. In balmy Ocean City freeze/thaw spalling risks are a lot lower than in cool Morristown or further north & west but you still have to stay ahead of the wood-rot issues where wood is in contact with cold-wet masonry.

This is a couple year old, but should still provide a decent foundation for you.

http://www.greenbuildingadvisor.com...-buildings