The Germans had succeeded in disarming and capturing much of the Italian armed forces because the Germans had known an armistice was close where as the Italian forces did not. Italians soldiers were given two choices: fight with the axis or surrender and go to a prison camp. Most choose the prison camp and the Germans captured about 650,000 Italian soldiers.

Italian POWs captured by the allies were given a similar choice: swear allegiance or don't. Those who did were given better jobs, better standard of living, and more freedom, but they were still considered POWs.

The fact that the Germans had seized most of the Italians equipment and taken most Italian soldiers meant that the new Italian government in the south would need some time to build up an army. In the meantime some Italian commanders began to fight back against the Germans. In Albania and Greece local Italian commanders fought back, sometimes joining with the local partisans. In Albania, one Italian commander had his head cut off and paraded on a bayonet for fighting back against the Germans. Many other Italian units formed anti-fascist partisan groups who would harass the German's and support the allies.

The allies were reluctant to allow the Italian army to grow stronger, mainly because they were worried that a strong Italian army would be a point of pride for the Italians and interfere with any post war plans that the British and Americans had for Italy. None the less the allies allowed the Italians to raise an army of about half a million men but only about 60,000 would be actual combat troops. They formed different combat groups and were attached to other allied units. For example the "Cremona" combat group was attached to the First Canadian Army; the new Italian army was used for offensive operations, but never alone, it was always attached or fighting with other allied units close by. The new army suffered from manpower problems as most Italians in the South were war weary and many didn't want to continue fighting; there was also regional divides, as the South didn't want to fight to liberate the North. They also were unable to supply themselves and had to rely on the allies, mainly the British, to do so.

Source:

The Fall of Mussolini, Italy, the Italians, and the Second World War by: Phillip Morgan

Other commenters are discussing Italian troops, but what you have to realise is that the critical difference was made not so much by the troops, but by the partisans, i.e. civilians who had taken up arms to fight on the Allied side.

The partisan organisations had obviously never been on Mussolini's side to begin with, even before the war: the assassination of Matteotti in 1924 made sure there was a huge leftist anti-fascist group in Italy who didn't consider Mussolini to be the legitimate head of state and, when the war started, fought against Mussolini much in the way the French Resistance fought against the German occupation.

When Italy signed the armistice with the Allied powers in 43, however, they really came to realise their full potential, combining guerrilla tactics and knowledge of the terrains, huge public support, and proper funding for equipment. Mussolini was arrested in 45, not by the state troops, but by the partisans.

By 1944, there were about 80,000 of them, when 50,000 of them had already been killed in action. Remember, these were civilians taking up arms and organising themselves into pseudo-military groups.

This, I believe, is one of the primary reasons why Italy, to this day, considers itself to have been firmly in the Allied camp: the fighting force between 43 and 45 was a people's army, not just a state army. The heroes were regular people.

edit: legal legitimate

There actually were plans in place for the Italian army to switch sides and fight with the Allies. However, mistakes in planning meant this did not happen.

As part of the original Armistice between the Allies and the Bodoglio government Italian troops, particularly in Rome, were to fight the Germans after the Armistice was announced. The US 82nd airbourne division was to drop into Rome to assist the Italian units there, while (in the rest of Italy) Italian forces were meant to oppose the German army.

But when General Carboni (the commander of the Italian forces in Rome) heard about the plan he - correctly - stated that, with the help of only one Allied division, his forces would be no match for the German forces stationed in the city (Students Parachute Corps). Therefore Carboni arranged for 2 extra Italian divisions to be bought into the city, and Badoglio signalled to Eisenhower asking for the announcement of the Armistice (and with it, the Italian change of side and 82nd drop on Rome) to be postponed from the 12th to the 15th.

Unbeknown to the Italians, the Allies were working off a different schedule all together - the announcement, the drop and the landings at Salerno were all to take place on the 8th, not the 12th as the Italians thought/assumed. When Eisenhower got the message from Bodoglio he assumed he had been double crossed.

Eisenhower went ahead with the original plan and announced the Armistace from Algiers on the 8th. When no announcement was made from Rome he also had the text of Badoglio's announcement read. Following this Badoglio realised there could be no delay and made his announcement an hour after Algiers had.

This action destroyed any chance of the majority of the Italian army fighting the Germans. As they had been working of the assumption the announcement would be on the 12th (and, after the message to Eisenhower, the 15th) the Italian high command had not issued instructions to its forces on how to act (largely through fear the Germans would get word of it). The announcement read by Algiers didn't give explicit instructions of how the Italian armed forces were to act - only that they were to cease fighting the Allies, but should defend themselves from aggression from any other party. Therefore Italian units that were not attacked by the Germans, but were merely disarmed by them, had no reason (and no instructions) to fight back.

And finally, as Carboni assumed the Italian forces in Rome quickly fell, and the government was forced to flee.

Source: The Battle for Italy by W. Jackson.

A qualified yes. The Italian cobelligerent forces weren't able to field large numbers of troops, and they were never trusted with anything vital by the allied supreme command, which doubted their loyalty for pretty clear reasons. But they did participate in some allied offensives, usually under US supervision, and performed acceptably.