Dnj, I have to dissagree. It has nothing to do with being a bigger man/woman. She has fired him from the husband position. So that's a no to breaking the ice. All conversations should be eather about the kids or the finances, other conversation should be avoided, at least until the healing process has done a couple of cycles.
Any breaking of the proverbial ice is uncomfortable and a LBS is inclined to read too much into the conversation. For instance, if the WS says she's feeling bad or going throug a rough patch, the LBS's brain turns this into a proof that the WS is missing him or even that she's realised the mistake she's made. THis could not be farther from the truth. If anything, she's only feeling sorry for herself and nothing more. In her mind she's intitled for everything, and more, and any opposition from the LBS is met with anger and bile.
By all means the LBS should be putting on a brave face, not overtly happy, because this will come across as phony. Snar remarks and anger should be controlled as they really do serve no purpose.
I found it best if the ex spouse is treated like a distant neighbour or a business associate, where you politely greet them but avoid any personal interaction.