You might need to know how to do this one day in your life. I never thought I would.
There is no easy way to set the row height of a table in MS Publisher. So it is quite easy to have your rows be set unevenly. I never found a distribute function either.
One work around is to set the row height using VBA:
Private Sub changeRows()
Dim i As Integer
i = 1
Dim RowHeight As Double
RowHeight = 15.5 'ThisDocument.Selection.ShapeRange(1).Table.Rows(i).Height
For i = 1 To ThisDocument.Selection.ShapeRange(1).Table.Rows.Count Step 1
ThisDocument.Selection.ShapeRange(1).Table.Rows(i).Height = RowHeight
Next
End Sub
This code only works if you have your row heights selected. The idea was taken from here, but modified to loop through the rows.