Just a collection of pics, if I can figure out how to load them all. The kissing photo includes her bff, Darwin, a lab-springer spaniel who is 6 mos. older than her. Actually, she's his puppy.
I can see why someone would think there was Terrier, but I'm not so sure about Basenji. (The only way to know for sure is to do a DNA test.) Both of your dogs look very similar. What breed, or mix, is the older one?
I think I see some of the basenji ears, especially in the second picture. I just want to grab them and rub them good! :) It's most likely that there is at least a black lab there too. Also it may be not the first "mix". If it is a generation over there may be more then one mix in there. But either way, Lilly is adorable! :):) It's awesome that she has a good forever home now.
Oh yeah, he looks way more like a b-mix to me than a lot of the pups listed as basenjis on Petfinder. And they mention he's not a barker. What a cutie! Someone go get this guy! :D
Look at the BRAT mixes:
http://basenjirescue.org/DOGS-MIXES/Default.htm
Check out Tia. I think that's what you are looking for. :)
Then look at Tyson and Shiloh. Not the right coloring, but similar build and coat….