Part of the issue with answering this question is defining what counts as a foreign intervention. The Congressional Research Service has published a report entitled Instances of Use of United States Armed Forces Abroad, 1798-2020, which is an attempt to "provide a rough survey of past U.S. military ventures abroad". However, it is questionable whether some of these deployments really count as interventions in foreign conflicts - for example, the list includes entries such as:
1904 - Tangiers, Morocco
A squadron demonstrated to force the release of a kidnapped Americans
Ion Hanford Perdicaris and Cromwell Varley. Marines were landed to
protect the consul general.
1922 - Turkey
A landing force was sent ashore with consent of both Greek and
Turkish authorities to protect American lives and property when the Turkish Nationalists entered
1948 - China
Marines were dispatched to Nanking to protect the American embassy when the city fell to
Communist troops, and to Shanghai to aid in the protection and evacuation of Americans.
It does, however, note the eleven times in its history that the US has formally declared war, as well as the number of informal declarations of war.
The instances differ greatly in number of forces, purpose, extent of
hostilities, and legal authorization. Eleven times in its history, the
United States has formally declared war against foreign nations. These
11 U.S. war declarations encompassed five separate wars: the war with
Great Britain declared in 1812; the war with Mexico declared in 1846;
the war with Spain declared in 1898; the First World War, during which
the United States declared war with Germany and with Austria-Hungary
during 1917; and World War II, during which the United States declared
war against Japan, Germany, and Italy in 1941, and against Bulgaria,
Hungary, and Rumania in 1942.
Some of the instances were extended
military engagements that might be considered undeclared wars. These
include the Undeclared Naval War with France from 1798 to 1800; the
First Barbary War from 1801 to 1805; the Second Barbary War of 1815;
the Korean War of 1950-1953; the Vietnam War from 1964 to 1973; the
Persian Gulf War of 1991; global actions against foreign terrorists
after the September 11, 2001, attacks on the United States; and the
war with Iraq in 2003. With the exception of the Korean War, all of
these conflicts received congressional authorization in some form
short of a formal declaration of war.
If we look at these conflicts, all formal declarations of war since 1900 have come under Democratic presidents - those related to WWI & II, while the informal declarations of war are more mixed; the Korean & Vietnam wars began under Democratic presidents, while the Gulf War, the response to the 9/11 attacks, and the Iraq war all came under Republicans; Bush Sr. & Jr. This would seem to be a fairly even split.
In an optimistic attempt to view this issue in a more data-focused manner, I've looked at the Militarized Interstate Disputes dataset maintained by the Correlates of War Project, which lists information about 'conflicts in which one or more states threaten, display, or use force against one or more other states'. I've narrowed the dataset down to conflicts which involved the US, began after 1900, and in which the hostility level reached a level of '4' - indicating use of force, rather than just a display of force.
Below is a graph of these conflicts, the size of each red or blue dot relating to the fatality level, and the color of each relating to the party of the President. On a purely numerical basis, Republican presidents oversaw 53 of these incidents, while Democratic presidents oversaw 41. However, when we look at the severity of the disputes, those which came under Democratic presidents reached, on average, a higher level of hostility and a higher fatality level.
Note - 'Interstate' refers to conflicts between two or more sovereign states, not two or more states within the USA.