I think [name_f]Claire[/name_f] and [name_f]Chloe[/name_f] sound lovely for sisters.
Obviously (I know this wasn’t part of your questions, but) if you do have any more children, then you would have to consider whether you’d continue the C trend or veer away.
If you did veer away from names starting with C, I would suggest using another sound for any future children that still tie in.
L names, -e ending sounds and soft R or K sounding names would all work well I think, such as:
[name_f]Lily[/name_f], [name_f]Lucy[/name_f], [name_f]Alice[/name_f], [name_u]Marie[/name_u] (maybe not), [name_f]Mabel[/name_f], [name_f]Mildred[/name_f], [name_u]Charlie[/name_u], [name_f]Charlotte[/name_f], [name_f]Elsie[/name_f], [name_f]Audrey[/name_f], [name_f]Sylvie[/name_f], [name_u]Louise[/name_u], [name_f]Daphne[/name_f], [name_f]Fleur[/name_f], [name_u]Henry[/name_u], [name_u]Ivy[/name_u], Jack/Jacques (where the C/K sound is at the end, still ties in) [name_f]Naomi[/name_f], [name_f]Amelie[/name_f], [name_f]Pearl[/name_f], [name_f]Olive[/name_f], [name_f]Emily[/name_f], [name_u]William[/name_u], etc.
What I might suggest is clicking on any of those names (as well as [name_f]Claire[/name_f] [name_f]Kate[/name_f] and [name_f]Chloe[/name_f] Anne) and looking at the 20 suggested similar names on Nameberry for inspiration. I always find a couple of gems that way that tie in nicely.
As for middle names for [name_f]Chloe[/name_f], I would suggest:
[name_f]Chloe[/name_f] [name_u]Anne[/name_u] (I agree with your husband, this one is my favourite out of [name_u]Marie[/name_u], [name_f]Rose[/name_f] and Anne)
[name_f]Chloe[/name_f] [name_u]Louise[/name_u]
[name_f]Chloe[/name_f] [name_f]Alice[/name_f]
[name_f]Chloe[/name_f] [name_u]Jean[/name_u]
[name_f]Chloe[/name_f] [name_f]Beatrice[/name_f]
[name_f]Chloe[/name_f] [name_f]Beatrix[/name_f]
[name_f]Chloe[/name_f] [name_f]Diane[/name_f]
[name_f]Chloe[/name_f] [name_f]Deirdre[/name_f]
[name_f]Chloe[/name_f] Maud/Maude
[name_f]Chloe[/name_f] [name_f]May[/name_f]
[name_f]Chloe[/name_f] [name_f]Josephine[/name_f]
[name_f]Chloe[/name_f] [name_f]Bridget[/name_f]
[name_f]Chloe[/name_f] [name_f]Bethany[/name_f]
[name_f]Chloe[/name_f] [name_f]Juliet[/name_f]
[name_f]Chloe[/name_f] [name_f]Elisabeth[/name_f]
[name_f]Chloe[/name_f] [name_f]Lucy[/name_f]
[name_f]Chloe[/name_f] [name_f]Margaret[/name_f]
[name_f]Chloe[/name_f] [name_f]Violet[/name_f]
[name_f]Chloe[/name_f] [name_f]Eleanor[/name_f]
I’m sure there are loads more that have escaped my mind!
But my favourites (that I think fit best with your guys’ style) are:
[name_f]Claire[/name_f] [name_f]Kate[/name_f] & [name_f]Chloe[/name_f] [name_u]Anne[/name_u]
[name_f]Claire[/name_f] [name_f]Kate[/name_f] & [name_f]Chloe[/name_f] [name_u]Louise[/name_u]
[name_f]Claire[/name_f] [name_f]Kate[/name_f] & [name_f]Chloe[/name_f] [name_f]Alice[/name_f]
[name_f]Claire[/name_f] [name_f]Kate[/name_f] & [name_f]Chloe[/name_f] [name_f]Violet[/name_f]
[name_f]Claire[/name_f] [name_f]Kate[/name_f] & [name_f]Chloe[/name_f] [name_f]May[/name_f]
Congratulations and good luck!