Please see http://mail.openjdk.java.net/pipermail/nashorn-dev/2015-November/005621.html

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I used NetBeans 8.0.2 and jdk 8 update 65 on Windows 7.  I think I managed to reproduce the issue you described.
Steps I used are as follows:

1) create a new NB project called "script_sample" with one Main.java in it as source:

import javax.script.*;

public class Main {
   public static void main(String[] args) throws Exception {
       ScriptEngineManager m = new ScriptEngineManager();
       ScriptEngine e = m.getEngineByName("nashorn");
       e.eval("load(\"" + args[0] + "\")");
       System.out.println("press any key to continue..");
       System.in.read();
       e.eval("load(\"" + args[0] + "\")");
   }
}

2) "clean and build" the NB project

3) create a simple script test.js with the following content (outside the NB project)

print("in test.js script");
var x = 33;
x++;
print(x);

3) in a command line shell (I used cygwin), start the java process with debugger server on - but not suspended at the start:

     java -cp script_sample/dist/script_sample.jar -agentlib:jdwp=server=y,suspend=n,transport=dt_socket Main test.js

The last command runs code up to the point of System.in.read call in Main.java

4) In NetBeans, open the test script file "test.js" and set breakpoint @ "print" call.

5) In NetBeans, use "Debug->Attach Debugger..." menu and specify the socket port printed by step (3)

5) enter a value for System.in.read() in command line shell.

6) No breakpoint hit @ test.js

But, if step (3) was modified to suspend process at start for debugger attach:

     java -cp script_sample/dist/script_sample.jar -agentlib:jdwp=server=y,suspend=y,transport=dt_socket Main test.js

The breakpoint in test.js enters (twice) once for each "load("test.js")" call.

So, there seems to be a bug somewhere (in NetBeans?). That said, there seems to be a simple workaround for this issue.
Within NB, set a breakpoint in Main.java (in addition to breakpoint in test.js) at second eval call  (line 10).  breakpoint is hit in Main.java.
At that point, keep hitting "Step Into" (F7) menu. It eventually lands in test.js -- and stops at the breakpoint in script!

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