You can find the monthly Levitus dataset here:
The available variables include salinity, temperature, potential temperature, and mixed layer depth. Once you have chosen the variable you need, click on "Data Selection" to select June and July. When you click on "Data Selection", the resulting page displays text boxes for each grid (X,Y,Z,T) of the dataset. Just type in "Jun to Jul" in the time grid text box and then click "Restrict Ranges" and "Stop Selecting".