As far as I'm aware you can't have more than one target set up in a castsequence (and therefore can't switch half way through).

But you might be able to do something similar by using /click (there's a long thread about using this method for stuff like dot rotations, but I can't remember who wrote it), you will need 3 macros for this to work though (and alternative is to have the heal bound to a modifier, but you may have other reasons for not wanting to do that).

So, here's my idea.
The macro on your toons main toolbar (i.e. the button you'll be pressing) has the following info in:

/click <whatever action button the dps castsequence macro is attached to>
/click <whatever action button the healing castsequence macro is attached to>

Then you have the following macros for dps and healing:

(dps macro)
/castsequence [target=tanks-target] CL, CL, CL, ,

(heal macro)
/castsequence [target=tank] , , , LHW

So you have empty commas wherever you want to use a spell from the other targetted castsequence (you may need to add more if you button mash though or use that key for tank abilities). With the empty comma nothing should happen in the first macro for that button press, which should allow the heal in the second macro to get cast.

Editing so this looks more like a helpful post and less like a notebook of scrawled ideas
A much simpler macro for the healing part would be /cast [target=tank] LHW as it won't cast if CL is underway

I think you could even change the first macro to

/click <dps macro action button>
/cast [target=tank] LHW

as theroetically the LHW should not cast until an empty comma comes up in the dps macro.

I would also like to say that this is completely untested, so I apologise if it doesn't work.