Show us a photo if you can. Red and White isn't necessarily the same as 'looks like a Shorthorn'.
CP is right about Ayrshire. Unless there's an awful lot of red factor hiding among NZ cows... the cross over b + w often comes out red. I've been told Ayrshire over Jersey is sometimes straight black (but I've got some small solid red cows bred that way)
HFxJ can be red and white or red, but usually isn't a first cross in those colours.
Any opinions from you overseas dairy cows on whether the red and white gene in Holsteins is linked to increased hardiness? I've seen that claim made in support of the red breeds including red holstein.