2d interpolation querying

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I want to interpolate two-dimensional data and be able to query from one dimension over time.

With one dimensional data, say m(t), I can use pp=pchip(t,m) where t is the known data locations and m the corresponding data points. I can then define a function mq = @(t) ppval(pp,t) and query m for any value of t in the future.

Now, I would like to do the same for two-dimensional data. Say I have 2d data, m(t,x). Then I want to be able to find an interpolated m(.,x) for any t (the values of x are fixed). The interp2 funciton seems like a possibility, but can not return piecewise polynomial structures for future evaluation like pchip does for me, and pchip does not have a 2d function.