I used your data and adapted the function to make it easy to demonstrate

In[3]:= x = {0.0, 0.1, 0.2, 0.2, 0.3, 0.3} 
y = {0.1, 0.2, 0.3, 0.4, 1.0, 1.5}
 z = {0.01, 0.02, 0.022, 0.023, 0.02344, 0.02345}

Out[3]= {0., 0.1, 0.2, 0.2, 0.3, 0.3}

Out[4]= {0.1, 0.2, 0.3, 0.4, 1., 1.5}

Out[5]= {0.01, 0.02, 0.022, 0.023, 0.02344, 0.02345}

In[7]:= myList = Transpose[{x, y, z}]

Out[7]= {{0., 0.1, 0.01}, {0.1, 0.2, 0.02}, {0.2, 0.3, 0.022}, {0.2, 
  0.4, 0.023}, {0.3, 1., 0.02344}, {0.3, 1.5, 0.02345}}

In[10]:= f[{x_, y_, z_}] := (1/(1 + z y)) Sin[x]

In[11]:= Map[f, myList]

Out[11]= {0., 0.0994357, 0.197367, 0.196858, 0.288752, 0.285479}

The trick is to use Transpose on the three lists to make a list of ordered triples.

I replaced p[x] with Sin[x] to make it easy for me.

You then Map[] the function over the list.

There may be a way to eliminate the braces in the argument list for the function, but I don't remember it off-hand.