According to the United States Census Bureau, the borough has a total area of 1.0 square mile (2.6 km2), of which 0.3 square miles (0.78 km2) is land and 0.7 square miles (1.8 km2), or 71.43%, is water.
As of the census of 2000, there were 1,711 people, 762 households, and 447 families residing in the borough. The population density was 6,156.7 people per square mile (2,359.4/km²). There were 817 housing units at an average density of 2,939.8/sq mi (1,126.6/km²). The racial makeup of the borough was 95.56% White, 1.40% African American, 0.23% Native American, 1.40% Asian, 0.76% from other races, and 0.64% from two or more races. Hispanic or Latino of any race were 3.45% of the population.
There were 762 households out of which 23.8% had children under the age of 18 living with them, 45.1% were married couples living together, 10.1% had a female householder with no husband present, and 41.3% were non-families. 34.4% of all households were made up of individuals and 9.3% had someone living alone who was 65 years of age or older. The average household size was 2.25 and the average family size was 2.91.
In the borough the population was spread out with 19.5% under the age of 18, 5.8% from 18 to 24, 33.0% from 25 to 44, 27.8% from 45 to 64, and 13.9% who were 65 years of age or older. The median age was 41 years. For every 100 females there were 94.9 males. For every 100 females age 18 and over, there were 93.7 males.
Woodmont is considered to be a generally affluent borough of Milford. As of a 2011 estimate, the median income for a household in the borough was $76,458, and the median income for a family was $97,500. The average income for a family was $125,760. The per capita income was $44,378.