returning false not stopping the submission of form

return false is working fine, the way you are calling that function is wrong.

<form action="post.php" method="post" onsubmit="doit()"> 

Just calls it, doesn't do anything with the return value

<form action="post.php" method="post" onsubmit="return doit()"> 
                                                ^

Will stop the form post on a false returned value.

Read this note on MSDN although it is not IE specific

You can override this event by returning false in the event handler. Use this capability to validate data on the client side to prevent invalid data from being submitted to the server. If the event handler is called by the onsubmit attribute of the form object, the code must explicitly request the return value using the return function, and the event handler must provide an explicit return value for each possible code path in the event handler function.

Now onto another important point.

Your if condition will only stop form submission when both the fields are blank, whereas it should do that even if any one of those two fields is blank. That && (AND) should be an || (OR), and at the end of your functions if nothing returned false, return true then.

onsubmit event accepts boolean values, since you are not returning anything so it assumes true by default. You need to add return in this event explicitly like mentioned below:

change

onsubmit="doit()"> 

to

onsubmit="return doit()">