Why is dichloromethane immiscible in water?
The physical causes of solubility of substances in each other can semiquantitatively be expressed by the Hansen solubility parameters.

$\begin{array}{}
\text{Water}:&amp;&amp;\delta_d=15.6&amp;\delta_p=16.0&amp;\delta_h=42.3&amp;R_0=47.8\\
\text{Dichloromethane}:&amp;&amp;\delta_d=18.2&amp;\delta_p=6.3 &amp; \delta_h=6.1&amp;R_0=20.2
\end{array}$

$$R_0=20.2,\ \ \ R_a=37.8$$

$$RED=\frac{R_a}{R_0}=1.87$$

RED &lt; 1 would show solubility of both substances in each other. But RED > 1, so both substances are little soluble in each other. 

The solubility parameters above show, the energies from polar and from hydrogen bridging bond intermolecular attractions are higher in water.

Generally, chlorinated hydrocarbons have lower energies from polar and hydrogen bridging bond intermolecular attractions.

The strongest hydrogen bridging bonds are formed between the atoms of the strongly electronegative elements $\ce{F}$, $\ce{O}$ and $\ce{N}$. But the atoms of other electronegative elements, e.g. $\ce{Cl}$-, $\ce{S}$- and $\ce{C}$-atoms, are capable of weak hydrogen bridging bonds at suitable molecular structure.

The atomic radii of the third period elements ($\ce{P}$, $\ce{S}$, $\ce{Cl}$) are much larger than those of the second period elements ($\ce{N}$, $\ce{O}$, $\ce{F}$). $\ce{Cl}$-atoms have lower charge density therefore. They are weaker proton acceptors therefore. 

Hydrogen bridging bonds can be proved e.g. by molecular spectroscopy.

Li Bian: Proton Donor Is More Important Than Proton Acceptor in Hydrogen Bond Formation: A Universal Equation for Calculation of Hydrogen Bond Strength. J. Phys. Chem. A 107 (2003) (51) 11517–11524

Weinhold, F.; Klein, R. A.: What is a hydrogen bond? Mutually consistent theoretical and experimental criteria for characterizing H-bonding interactions. Mol. Phys. 110 (2012) (9-10) 565-579 

Gilli, G.; Gilli, P.: The Nature of the Hydrogen Bond: Outline of a Comprehensive Hydrogen Bond Theory. Oxford University Press, Oxford, 2013